Questions About Brass vs PVC Tub Drain Assembly To ABS Trap

I have a couple of novice questions about tub drains. Because of the tub "the boss" picked out, I think I need to replace the existing drain (Brass to ABS trap):

with a Kohler slot-type overflow drain:

I'm a little confused about the size of the Brass tailpiece vs the ABS trap fitting it slides into. The Inside Diameter of the ABS fitting and the Outside Diameter of the existing tailpiece are both right at 1 1/2", with the tailpiece OD maybe a couple of thousandths smaller according to my caliper (obviously, or it wouldn't fit). Is Brass sizing one of the cases where nominal size refers to O.D. rather than I.D., or is this some kind of special tailpipe made to fit into 1 1/2 ABS? In other words, if I order the Kohler drain (which calls out the tailpiece as 1 1/2 O.D.), should I expect it to be the same slip fit into the ABS, using the same type washer and nut as the existing?

Also, the Kohler drain is available in PVC as well as Brass, for about $50 less:

Obviously, 1 1/2" PVC wouldn't fit into the ABS trap because the O.D. would be too large. Is there some kind of transition from PVC to ABS I could use to save a few bucks, or are there other advantages to sticking with the Brass?

If the PVC drain is specified as Schedule 40 (normal ABS/PVC/Galv Drain/Waste/Vent piping size), then it won't fit. Schedule 40 "glued" tub drains are used where there is no
access to the drain. Brass tubular size drains (no matter what they're made of) with slip-joint fittings require access. The photo you posted looks like it has a Schedule
40 santee meant to be glued to Schedule 40 PVC trap/piping below.